Bleeding Heart Martini

Chill 4 martini glasses in the freezer or fill with ice water and let sit until frosty, about 5 minutes (pour out water). Add the vermouth, dividing evenly; swirl to coat the glasses, then pour out. Add gin to a cocktail shaker filled with ice. Shake vigorously until chilled; divide among chilled glasses. Garnish each with a skewered pickled baby beet, and serve immediately.